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This paper is concerned with the construction and implementation of a continuous fourth order trigonometrically fitted method on oscillatory initial value problems (IVPs). The continuous scheme is used to generate four discrete methods as by products. The four discrete schemes are weighted thesame and used via the Block Unification Approach to obtain approximate solutions to first order IVPs with oscillating solutions. The convergence of the method is established and two test problems are given to show the accuracy and computational efficiency of the scheme.

A FOURTH ORDER TRIGONOMETRICALLY FITTED METHOD WITH THE BLOCK UNIFICATION IMPLEMENTATION APPROACH FOR OSCILLATORY INITIAL VALUE PROBLEMS